Tottenham are fifth in the table at the moment with 24 points from 13 matches, just four points behind leaders Leicester City.
The North London outfit are only two points behind third-place Manchester City and fourth-place Arsenal and just three behind Manchester United, who are currently second.
Former Tottenham midfielder Redknapp, though, does not fancy Mauricio Pochettino’s side’s chances of winning the league this season.
"I don't think they can win the title, but I think they should aim for top four,” the Englishman told Sky Sports. "I just don't think they're good enough and there are much better teams.
“Without taking anything away from what they're doing here because it's fantastic, but I don't think they're ready to win the league yet.”
Former Tottenham chairman Alan Sugar has also cast doubt on Tottenham’s chances to challenge for the league, but ex-Manchester United and Liverpool striker Michael Owen has suggested that Spurs could be the dark horse.
Liking the look of Spurs. Dark horses for the title? https://t.co/KLUCtITICd— michael owen (@themichaelowen) November 22, 2015
Well it is possible but a big ask https://t.co/HjdOHCXYT1— Lord Sugar (@Lord_Sugar) November 22, 2015
@Lord_Sugar Another great win for the spurs , do you think we can win the league this season ?— Shane Oconnor (@aussierules13) November 22, 2015
The Premier League title race has been very unpredictable so far this season, with reigning champions Chelsea now clearly out of the race.
Tottenham’s main target since the start of the campaign was to get into the top four, and that should remain their objective for now.
Arsenal, United and City all have better teams than Tottenham, who should not get carried away and take it game by game.